Number theoretic properties of the commutative ring Zn

This paper deals with the number theoretic properties of nonunit elements of the ring Zn. Let D be the set of all nontrivial divisors of a positive integer n. Let D1 and D2 be the subsets of D having the least common multiple which are incongruent to zero modulo n with every other element of D and congruent to zero modulo n with at least one another element of D, respectively. Then D can be written as the disjoint union of D1 and D2 in Zn. We explore the results on these sets based on all the characterizations of n. We obtain a formula for enumerating the cardinality of the set of all nonunit elements in Zn whose principal ideals are equal. Further, we present an algorithm for enumerating these sets of all nonunit elements.